Reference : Contributions to the asymptotic study of Hermite driven processes
Dissertations and theses : Doctoral thesis
Physical, chemical, mathematical & earth Sciences : Mathematics
Contributions to the asymptotic study of Hermite driven processes
Tran, Thi Thanh Diu [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > > ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
University of Luxembourg, ​​Luxembourg
Docteur en Mathématiques
Nourdin, Ivan mailto
Thalmaier, Anton mailto
Peccati, Giovanni mailto
Réveillac, Anthony mailto
Tudor, Ciprian mailto
[en] Non-central limit theorems ; Limit theorems ; Hermite process ; Rosenblatt process ; Hermite Ornstein-Uhlenbeck process ; Multiple Wiener-Itô integrals
[en] This thesis consists of two parts.
Part I is an introduction to Hermite processes, Hermite random fields, Fisher information and to the papers constituting the thesis. More precisely, in Section 1 we introduce Hermite processes in a nutshell, as well as some of its basic properties. It is the necessary background for the articles [a] and [c]. In Section 2 we consider briefly the multiparameter Hermite random fields and we study some less elementary facts which are used in the article [b]. In section 3, we recall some terminology about Fisher information related to the article [d]. Finally, our articles [a] to [d] are summarised in Section 4.
Part II consists of the articles themselves: [a] T.T. Diu Tran (2017): Non-central limit theorem for quadratic functionals of Hermite-driven long memory moving average processes. Stochastic and Dynamics, 18, no. 4. [b] T.T. Diu Tran (2016): Asymptotic behavior for quadratic variations of nonGaussian multiparameter Hermite random fields. Under revision for Probability and Mathematical Statistics. [c] I. Nourdin, T.T. Diu Tran (2017): Statistical inference for Vasicek-type model driven by Hermite processes. Submitted to Stochastic Process and their Applications. [d] T.T. Diu Tran (2017+): Fisher information and multivariate Fouth Moment Theorem. Main results have already been obtained. It should be submitted soon.
University of Luxembourg - UL

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